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The instability and breaking of deep-water waves

Published online by Cambridge University Press:  20 April 2006

W. K. Melville
W. K. Melville
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, and Massachusetts Institute of Technology, Cambridge
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Abstract

An experimental study of the evolution to breaking of a nonlinear deep-water wave train is reported. Two distinct regimes are found. For ak [les ] 0·29 the evolution is sensibly two-dimensional with the Benjamin-Feir instability leading directly to breaking as found by Longuet-Higgins & Cokelet (1978). The measured side-band frequencies agree very well with those predicted by Longuet-Higgins (1978b). It is found that the evolution of the spectrum is not restricted to a few discrete frequencies but also involves a growing continuous spectrum, and the description of the evolution as a recurrence phenomenon is incomplete. It is found that the onset of breaking corresponds to the onset of the asymmetric development of the side bands about the fundamental frequency and its higher harmonics. This asymmetric evolution, which ultimately leads to the shift to lower frequency first reported by Lake et al. (1977), is interpreted in terms of Longuet-Higgins’ (1978b) breaking instability. For ak [ges ] 0·31 a full three-dimensional instability dominates the Benjamin-Feir instability and leads rapidly to breaking. Preliminary measurements of this instability agree very well with the recent results of McLean et al. (1981).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 165 - 185
Copyright
© 1982 Cambridge University Press

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